
\section{Research Projects}
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	\cmmnt{\textit{(3D)²}} \textbf{Vector Nonlinear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} \cmmnt{\newline \phantom{i} \newline \vspace{3pt} { \small \color{color-detail} decks } \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/2__Side_Projects/6.1__\%E4\%B8\%93\%E9\%A2\%98\%E7\%A0\%94\%E8\%AE\%A8\%E8\%AF\%BE\%20-\%20\%E4\%BB\%BB\%E6\%84\%8F\%20\%CE\%B5\%20\%E7\%94\%B5\%E4\%BB\%8B\%E8\%B4\%A8\%E4\%B8\%AD\%E7\%9A\%84\%E7\%9F\%A2\%E9\%87\%8F\%E7\%BA\%BF\%E6\%80\%A7\%E3\%80\%81\%E9\%9D\%9E\%E7\%BA\%BF\%E6\%80\%A7\%E8\%A7\%92\%E8\%B0\%B1\%20-\%20\%E6\%9C\%B1\%E7\%B4\%AB\%E8\%80\%80\%E9\%87\%91\%C2\%B7\%E7\%B4\%AB_\%E2\%86\%90_Python__3.0_year_-_2023.5.9.pdf}{\underline{1}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/7.1__\%E4\%B8\%AD\%E6\%9C\%9F\%E7\%AD\%94\%E8\%BE\%A9_\%E8\%B0\%A2\%E5\%B0\%98\%E7\%AB\%B9_\%E2\%86\%90_Python__3.5_year_-_2023.12.28.pdf}{\underline{2}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/8.1__\%E9\%AB\%98_N.A._\%E7\%9F\%A2\%E9\%87\%8F_\%E7\%B4\%A7\%E8\%81\%9A\%E7\%84\%A6_\%E2\%86\%90_Python__4.0_year_-_2024.3.12.pdf}{\underline{3}} \ ... \ \raisebox{-0.05\height}{\color{black!50}\faGithub}} & \textbf{Solving} \dbox{\colorbox{white}{\small $\left[ \left( \boldsymbol{\nabla} \times \right)^2 - k^{2}_{0} \;\! \bar{\bar{\boldsymbol{\varepsilon}}} \;\! \cdot \right] \! {\color{magenta} \boldsymbol{E} \! \left( \boldsymbol r \right)} = k^{2}_{0} \;\! \bar{\bar{\bar{\boldsymbol \chi}}} \colon \! \mathcal F^{-1}_\omega \! \left[ \widetilde{\boldsymbol E}_\mathrm{p} \widetilde{\boldsymbol E}_\mathrm{p} \right] \! \left( \boldsymbol r \right)$}} \textbf{analytically} \hfill 2023.05 \textendash \newline \vspace{2pt} $\bullet$ {\small First \& fastest white box solver ever for this inhomogeneous $\mathbb{C}^3_{\Yup} \! \left( \mathbb{R}^3_{\Yup} \right)$ wave equation} \cmmnt{ \hfill \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.2__\%E7\%BB\%B4\%E7\%89\%B9\%E6\%A0\%B9\%E6\%96\%AF\%E5\%9D\%A6_\%E2\%86\%90_Python\%2BVisio\%2BBookxNote_Pro\%2BLabView\%2BLatex__3.0_year_-_2023.6.9.pdf}{\small \color{color-detail} [\hspace{1pt}decks\hspace{2pt}{\color{black!50}\faGithub}\hspace{1pt}]} } \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small or other similar equations, with unprecedented efficiency-accuracy product} \newline \vspace{-4pt} $\bullet$ {\small No competitors for the time being: other methods or software including} \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small k-space RK4, pseudo-spectral, SSF, Green's Function methods, FDTD, COMSOL...} \newline \vspace{-4pt} $\bullet$ {\small Reproduced well-known papers, all of which provide either zero or wrong theory:} \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://www.nature.com/articles/s41566-020-0691-0}{\color{blue} Nat.Photo.} {\color{color-detail} \footnotesize \#proven theoratically wrong by this project \#femtosecond pump} } \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/oe/abstract.cfm?uri=oe-22-18-21347}{\color{blue} O.E.} {\color{color-detail} \footnotesize \href{https://link.aps.org/doi/10.1103/PhysRev.184.895}{\#Bloembergen's} \href{https://link.aps.org/doi/10.1103/PhysRevA.18.2592}{legacy2} \#experiment} $|$ \href{https://opg.optica.org/ome/abstract.cfm?uri=ome-14-1-92}{\color{blue} O.M.E.} {\color{color-detail} \footnotesize \#z-component} } \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://www.semanticscholar.org/paper/Propagation-of-high-order-circularly-polarized-and-Belyi-Khilo/82cc32a5c51169c5a7cbeeac2f26ac2ef4abe703}{\color{blue} O.E.} $|$ \href{https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=24baf99257608a593cc5f6ad59b7510dcdff9acc}{\color{blue} Q.E.} {\color{color-detail} \footnotesize \#high N.A. \#$\bar{\bar{\bar{\boldsymbol \chi}}}$ anisotropy} } \hfill { \small \color{color-detail} decks } \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/2__Side_Projects/6.1__\%E4\%B8\%93\%E9\%A2\%98\%E7\%A0\%94\%E8\%AE\%A8\%E8\%AF\%BE\%20-\%20\%E4\%BB\%BB\%E6\%84\%8F\%20\%CE\%B5\%20\%E7\%94\%B5\%E4\%BB\%8B\%E8\%B4\%A8\%E4\%B8\%AD\%E7\%9A\%84\%E7\%9F\%A2\%E9\%87\%8F\%E7\%BA\%BF\%E6\%80\%A7\%E3\%80\%81\%E9\%9D\%9E\%E7\%BA\%BF\%E6\%80\%A7\%E8\%A7\%92\%E8\%B0\%B1\%20-\%20\%E6\%9C\%B1\%E7\%B4\%AB\%E8\%80\%80\%E9\%87\%91\%C2\%B7\%E7\%B4\%AB_\%E2\%86\%90_Python__3.0_year_-_2023.5.9.pdf}{\underline{1}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/7.1__\%E4\%B8\%AD\%E6\%9C\%9F\%E7\%AD\%94\%E8\%BE\%A9_\%E8\%B0\%A2\%E5\%B0\%98\%E7\%AB\%B9_\%E2\%86\%90_Python__3.5_year_-_2023.12.28.pdf}{\underline{2}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/8.1__\%E9\%AB\%98_N.A._\%E7\%9F\%A2\%E9\%87\%8F_\%E7\%B4\%A7\%E8\%81\%9A\%E7\%84\%A6_\%E2\%86\%90_Python__4.0_year_-_2024.3.12.pdf}{\underline{3}} \ ... \ \href{https://github.com/ChenZhu-Xie/PhD_academia}{\raisebox{-0.05\height}{\color{black!50}\faGithub}} \\ \Gap\Gap\Gap
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	\textbf{Complex Vector Linear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} \cmmnt{\newline \phantom{i} \newline \vspace{3pt} { \small \color{color-detail} decks } \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/5.1__NLAST\%EF\%BC\%9A\%E9\%87\%8D\%E7\%8E\%B0\%E8\%BF\%87\%E5\%8E\%BB\%EF\%BC\%88\%E5\%B7\%B2\%E7\%9F\%A5\%EF\%BC\%89\%E3\%80\%81\%E9\%A2\%84\%E6\%B5\%8B\%E6\%9C\%AA\%E6\%9D\%A5\%EF\%BC\%88\%E6\%9C\%AA\%E7\%9F\%A5\%EF\%BC\%89\%EF\%BC\%8C\%E4\%B8\%80\%E7\%BB\%9F\%E5\%BD\%93\%E4\%B8\%8B\%EF\%BC\%88\%E5\%85\%A8\%E7\%9F\%A5\%EF\%BC\%89_\%E2\%86\%90_Python__2.5_year_-_2022.9.28.pdf}{\underline{1}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.1__\%E6\%B0\%B4\%E5\%BD\%A9\%E8\%8A\%B1\%E9\%B8\%9F_\%E2\%86\%90_Python__3.0_year_-_2023.3.27.pdf}{\underline{2}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.2__\%E7\%BB\%B4\%E7\%89\%B9\%E6\%A0\%B9\%E6\%96\%AF\%E5\%9D\%A6_\%E2\%86\%90_Python\%2BVisio\%2BBookxNote_Pro\%2BLabView\%2BLatex__3.0_year_-_2023.6.9.pdf}{\underline{3}} \ ... \ \raisebox{-0.05\height}{\color{black!50}\faGithub}} & \textbf{Analytic} \colorbox{white}{\small $ {\color{magenta} \boldsymbol{E} \! \left( \boldsymbol r \right)} \in \mathbb{C}^3_{\Yup} \! \left( \mathbb{R}^3_{\Yup} \right) $} to \dbox{\colorbox{white}{\small $\left[ \left( \boldsymbol{\nabla} \times \right)^2 - k^{2}_{0} \;\! \bar{\bar{\boldsymbol{\varepsilon}}} \;\! \cdot \right] \! {\color{magenta} \boldsymbol{E} \! \left( \boldsymbol r \right)} = \boldsymbol{0}$}} \textbf{where} \colorbox{white}{$\varepsilon_{ij} \in \mathbb{C}$} \hfill 2023.02 \textendash \newline \vspace{2pt} $\bullet$ {\small Drawing insights from \href{https://royalsocietypublishing.org/doi/10.1098/rspa.2003.1155}{\color{blue} PRS.A.} {\color{color-detail} \footnotesize \#\href{https://en.wikipedia.org/wiki/Michael_Berry_(physicist)}{M.V.Berry}'s legacy} $|$ \href{https://opg.optica.org/aop/abstract.cfm?uri=aop-6-4-368}{\color{blue} A.O.P.} $|$ \href{http://link.springer.com/10.1007/s00340-016-6512-y}{\color{blue} A.P.B.} $|$ \href{https://linkinghub.elsevier.com/retrieve/pii/S002240730500066X}{\color{blue} J.QSRT.} } \cmmnt{\hfill \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.1__\%E6\%B0\%B4\%E5\%BD\%A9\%E8\%8A\%B1\%E9\%B8\%9F_\%E2\%86\%90_Python__3.0_year_-_2023.3.27.pdf}{\small \color{color-detail} [\hspace{1pt}decks\hspace{2pt}{\color{black!50}\faGithub}\hspace{1pt}]}} \newline \vspace{-4pt} $\bullet$ {\small Next generation will come really close to the exact solution with highly !hermitian $\bar{\bar{\boldsymbol{\varepsilon}}}$} \newline \vspace{-4pt} $\bullet$ {\small Reproduced well-known papers, some are purely experimental (too hard to model):} \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/abstract.cfm?URI=josa-68-8-1098}{\color{blue} J.O.S.A.} {\color{color-detail} \footnotesize \href{https://en.wikipedia.org/wiki/Nicolaas_Bloembergen}{\#Bloembergen's} \href{https://link.aps.org/doi/10.1103/PhysRevA.18.2592}{legacy1}} $|$ \href{https://iopscience.iop.org/article/10.1088/2040-8978/17/7/075603}{\color{blue} J.O.} $|$ \href{https://linkinghub.elsevier.com/retrieve/pii/S0925346717304809}{\color{blue} O.M.} $|$ \href{https://linkinghub.elsevier.com/retrieve/pii/S0925346722003871}{\color{blue} O.M.} $|$ \href{https://iopscience.iop.org/article/10.1088/2040-8978/16/7/075702/meta}{\color{blue} J.O.} $|$ \href{https://onlinelibrary.wiley.com/doi/10.1002/lpor.201600112}{\color{blue} L.P.R.} } \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/josaa/abstract.cfm?uri=josaa-27-8-1828}{\color{blue} JOSA.A.} $|$ \href{https://opg.optica.org/oe/fulltext.cfm?uri=oe-17-20-17970}{\color{blue} O.E.} {\color{color-detail} \footnotesize \#tightly focus \#$\bar{\bar{\boldsymbol{\varepsilon}}}$ anisotropy} $|$ \href{http://www.nature.com/articles/s41377-020-00362-z}{\color{blue} Light.Sci.App.} $|$ \href{https://opg.optica.org/abstract.cfm?URI=oe-26-8-9840}{\color{blue} O.E.} } \hfill { \small \color{color-detail} decks } \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/5.1__NLAST\%EF\%BC\%9A\%E9\%87\%8D\%E7\%8E\%B0\%E8\%BF\%87\%E5\%8E\%BB\%EF\%BC\%88\%E5\%B7\%B2\%E7\%9F\%A5\%EF\%BC\%89\%E3\%80\%81\%E9\%A2\%84\%E6\%B5\%8B\%E6\%9C\%AA\%E6\%9D\%A5\%EF\%BC\%88\%E6\%9C\%AA\%E7\%9F\%A5\%EF\%BC\%89\%EF\%BC\%8C\%E4\%B8\%80\%E7\%BB\%9F\%E5\%BD\%93\%E4\%B8\%8B\%EF\%BC\%88\%E5\%85\%A8\%E7\%9F\%A5\%EF\%BC\%89_\%E2\%86\%90_Python__2.5_year_-_2022.9.28.pdf}{\underline{1}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.1__\%E6\%B0\%B4\%E5\%BD\%A9\%E8\%8A\%B1\%E9\%B8\%9F_\%E2\%86\%90_Python__3.0_year_-_2023.3.27.pdf}{\underline{2}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.2__\%E7\%BB\%B4\%E7\%89\%B9\%E6\%A0\%B9\%E6\%96\%AF\%E5\%9D\%A6_\%E2\%86\%90_Python\%2BVisio\%2BBookxNote_Pro\%2BLabView\%2BLatex__3.0_year_-_2023.6.9.pdf}{\underline{3}} \ ... \ \href{https://github.com/ChenZhu-Xie/PhD_academia}{\raisebox{-0.05\height}{\color{black!50}\faGithub}} \\ \Gap\Gap\Gap
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	\textbf{Real Scalar Nonlinear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} \cmmnt{\newline \phantom{i} \newline \vspace{3pt} { \small \color{color-detail} decks } \href{https://github.com/ChenZhu-Xie/postgraduate_academia/blob/main/1__Group_Meeting/4.1__NLAST_v1.0_\%E2\%86\%90_Python\%2BBookxNote_Pro__2.0_year_-_2022.3.4.pdf}{\underline{1}} \href{https://github.com/ChenZhu-Xie/postgraduate_academia/blob/main/1__Group_Meeting/4.2__NLAST_scalar_\%E2\%86\%90_Python\%2BBookxNote_Pro__2.0_year_-_2022.6.9.pdf}{\underline{2}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/2__Side_Projects/5.1__NLAST_Raman_Nath_\%E2\%86\%90_Python__2.5_year_-_2022.11.26.pdf}{\underline{3}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/2__Side_Projects/7.2__\%E9\%87\%8F\%E5\%AD\%90\%E5\%B0\%8F\%E7\%BB\%84\%E4\%BC\%9A\%EF\%BC\%9A\%E4\%B8\%8B\%E8\%BD\%AC\%E6\%8D\%A2_\%E6\%B3\%A2\%E7\%9F\%A2\%E5\%8C\%B9\%E9\%85\%8D\%E5\%9B\%BE_\%E2\%86\%90_Python\%2BGeoGebra__3.5_year_-_2023.11.30.pdf}{\underline{4}} \ ... \ \raisebox{-0.05\height}{\color{black!50}\faGithub}} & \textbf{Closed-form} \colorbox{white}{\small $ {\color{magenta} E_3 \! \left( \boldsymbol r \right)} \in \mathbb{C} \! \left( \mathbb{R}^3_{\Yup} \right) $} in \dbox{\colorbox{white}{\small $\Bigl[ \boldsymbol{\nabla}^2 + k^{2}_{3} \Bigr] {\color{magenta} E_3 \! \left( \boldsymbol r \right)} = - k^{2}_{03} \;\! \chi(\boldsymbol r) E_1(\boldsymbol r) E_2(\boldsymbol r)$}} \hfill 2022.02 \textendash \newline \vspace{2pt} $\bullet$ {\small Solving this multivariable/field nonlinear convolution equation on my own} \cmmnt{\hfill \href{https://github.com/ChenZhu-Xie/postgraduate_academia/blob/main/1__Group_Meeting/4.2__NLAST_scalar_\%E2\%86\%90_Python\%2BBookxNote_Pro__2.0_year_-_2022.6.9.pdf}{\small \color{color-detail} [\hspace{1pt}decks\hspace{2pt}{\color{black!50}\faGithub}\hspace{1pt}]}} \newline \vspace{-4pt} $\bullet$ {\small Strong alternative to Green's Function, pseudo-spectral, split-step Fourier methods} \newline \vspace{-4pt} $\bullet$ {\small Reproduced well-known papers \& models with maximum accuracy \& efficiency:} \cmmnt{\hfill \href{https://github.com/ChenZhu-Xie/NLAST}{\small \color{color-detail} [\hspace{1pt}repo\hspace{2pt}{\color{black!50}\faGithub}\hspace{1pt}]}} \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.143901}{\color{blue} P.R.L.} {\color{color-detail} \footnotesize \#Green} $|$ \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.023603}{\color{blue} P.R.L.} {\color{color-detail} \footnotesize \#experiment \#quantum} $|$ \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.93.133904}{\color{blue} P.R.L.} {\color{color-detail} \footnotesize \#experiment \#scatter} $|$ \href{https://link.aps.org/doi/10.1103/PhysRevLett.120.067601}{\color{blue} P.R.L.} } \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://onlinelibrary.wiley.com/doi/10.1002/lpor.201900321}{\color{blue} L.P.R.} {\color{color-detail} \footnotesize \#SSF \#quantum} $|$ \href{https://sourceforge.net/projects/rcwa-1d/files/anisotropic_rcwa}{Matlab} {\color{color-detail} \footnotesize \#RCWA} $|$ \href{http://aip.scitation.org/doi/10.1063/1.4934488}{\color{blue} A.P.L.} {\color{color-detail} \footnotesize \#femtosecond pump} } \newline \vspace{-4pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/abstract.cfm?URI=ol-42-21-4387}{\color{blue} O.L.} $|$ \href{https://link.aps.org/doi/10.1103/PhysRevA.101.023834}{\color{blue} P.R.A.} } \hfill { \small \color{color-detail} decks } \href{https://github.com/ChenZhu-Xie/postgraduate_academia/blob/main/1__Group_Meeting/4.1__NLAST_v1.0_\%E2\%86\%90_Python\%2BBookxNote_Pro__2.0_year_-_2022.3.4.pdf}{\underline{1}} \href{https://github.com/ChenZhu-Xie/postgraduate_academia/blob/main/1__Group_Meeting/4.2__NLAST_scalar_\%E2\%86\%90_Python\%2BBookxNote_Pro__2.0_year_-_2022.6.9.pdf}{\underline{2}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/2__Side_Projects/5.1__NLAST_Raman_Nath_\%E2\%86\%90_Python__2.5_year_-_2022.11.26.pdf}{\underline{3}} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/2__Side_Projects/7.2__\%E9\%87\%8F\%E5\%AD\%90\%E5\%B0\%8F\%E7\%BB\%84\%E4\%BC\%9A\%EF\%BC\%9A\%E4\%B8\%8B\%E8\%BD\%AC\%E6\%8D\%A2_\%E6\%B3\%A2\%E7\%9F\%A2\%E5\%8C\%B9\%E9\%85\%8D\%E5\%9B\%BE_\%E2\%86\%90_Python\%2BGeoGebra__3.5_year_-_2023.11.30.pdf}{\underline{4}} \ ... \ \href{https://github.com/ChenZhu-Xie/PhD_academia}{\raisebox{-0.05\height}{\color{black!50}\faGithub}}
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%	\textbf{3D Vector Nonlinear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} & \textbf{Solving} \dbox{\colorbox{white}{\small $\left[ \left( \boldsymbol{\nabla} \times \right)^2 - k^{2}_{0} \;\! \bar{\bar{\boldsymbol{\varepsilon}}} \;\! \cdot \right] \! {\color{magenta} \boldsymbol{E} \! \left( \boldsymbol r \right)} = k^{2}_{0} \;\! \bar{\bar{\bar{\boldsymbol \chi}}} \colon \! \mathcal F^{-1}_\omega \! \left[ \widetilde{\boldsymbol E}_\mathrm{p} \widetilde{\boldsymbol E}_\mathrm{p} \right] \! \left( \boldsymbol r \right)$}} \textbf{analytically} \newline \vspace{3pt} $\bullet$ {\small The first and fastest white box solver ever for this inhomogeneous wave equation} \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small or other similar equations, with unprecedented efficiency-accuracy product} \newline \vspace{-3pt} $\bullet$ {\small No competitors for the time being: other methods or software including} \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small k-space RK4, pseudo-spectral, SSF, Green's Function methods, FDTD, COMSOL...} \newline \vspace{-3pt} $\bullet$ {\small Reproduced well-known papers, all of which provide either zero or wrong theory:} \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://www.nature.com/articles/s41566-020-0691-0}{\color{blue} N.P.} {\color{color-detail} \footnotesize \#proven theoratically wrong by this project \#femtosecond pump} } \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/oe/abstract.cfm?uri=oe-22-18-21347}{\color{blue} O.E.} {\color{color-detail} \footnotesize \href{https://link.aps.org/doi/10.1103/PhysRev.184.895}{\#Bloembergen's} \href{https://link.aps.org/doi/10.1103/PhysRevA.18.2592}{legacy2} \#experiment} $|$ \href{https://opg.optica.org/ome/abstract.cfm?uri=ome-14-1-92}{\color{blue} O.M.E.} {\color{color-detail} \footnotesize \#z-component} } \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://www.semanticscholar.org/paper/Propagation-of-high-order-circularly-polarized-and-Belyi-Khilo/82cc32a5c51169c5a7cbeeac2f26ac2ef4abe703}{\color{blue} O.E.} $|$ \href{https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=24baf99257608a593cc5f6ad59b7510dcdff9acc}{\color{blue} Q.E.} {\color{color-detail} \footnotesize \#high N.A. \#$\bar{\bar{\bar{\boldsymbol \chi}}}$ anisotropy} } & 2023.05 \newline \vspace{7pt} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.2__\%E7\%BB\%B4\%E7\%89\%B9\%E6\%A0\%B9\%E6\%96\%AF\%E5\%9D\%A6_\%E2\%86\%90_Python\%2BVisio\%2BBookxNote_Pro\%2BLabView\%2BLatex__3.0_year_-_2023.6.9.pdf}{\raisebox{-0.05\height}{\color{black!50}\faGithub}} \\ \Gap\Gap\Gap
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%	\textbf{Complex Vector Linear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} & \textbf{Analytic solution} \colorbox{white}{\small $ {\color{magenta} \boldsymbol{E} \! \left( \boldsymbol r \right)} $} to \dbox{\colorbox{white}{\small $\left[ \left( \boldsymbol{\nabla} \times \right)^2 - k^{2}_{0} \;\! \bar{\bar{\boldsymbol{\varepsilon}}} \;\! \cdot \right] \! {\color{magenta} \boldsymbol{E} \! \left( \boldsymbol r \right)} = \boldsymbol{0}$}} \textbf{where} \colorbox{white}{$\varepsilon_{ij} \in \mathbb{C}$} \newline \vspace{3pt} $\bullet$ {\small Drawing insights from \href{https://royalsocietypublishing.org/doi/10.1098/rspa.2003.11558}{\color{blue} PRS.A.} {\color{color-detail} \footnotesize \#\href{https://en.wikipedia.org/wiki/Michael_Berry_(physicist)}{M.V.Berry}'s legacy} $|$ \href{https://opg.optica.org/aop/abstract.cfm?uri=aop-6-4-368}{\color{blue} A.O.P.} $|$ \href{http://link.springer.com/10.1007/s00340-016-6512-y}{\color{blue} A.P.B.} $|$ \href{https://linkinghub.elsevier.com/retrieve/pii/S002240730500066X}{\color{blue} J.QSRT.} } \newline \vspace{-3pt} $\bullet$ {\small The next generation of this project will come really close to the exact solution } \newline \vspace{-3pt} $\bullet$ {\small Reproduced well-known papers, some are purely experimental (too hard to model):} \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/abstract.cfm?URI=josa-68-8-1098}{\color{blue} J.O.S.A.} {\color{color-detail} \footnotesize \href{https://en.wikipedia.org/wiki/Nicolaas_Bloembergen}{\#Bloembergen's} \href{https://link.aps.org/doi/10.1103/PhysRevA.18.2592}{legacy1}} $|$ \href{https://iopscience.iop.org/article/10.1088/2040-8978/17/7/075603}{\color{blue} J.O.} $|$ \href{https://linkinghub.elsevier.com/retrieve/pii/S0925346717304809}{\color{blue} O.M.} $|$ \href{https://linkinghub.elsevier.com/retrieve/pii/S0925346722003871}{\color{blue} O.M.} $|$ \href{https://iopscience.iop.org/article/10.1088/2040-8978/16/7/075702/meta}{\color{blue} J.O.} $|$ \href{https://onlinelibrary.wiley.com/doi/10.1002/lpor.201600112}{\color{blue} L.P.R.} } \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://opg.optica.org/josaa/abstract.cfm?uri=josaa-27-8-1828}{\color{blue} JOSA.A.} $|$ \href{https://opg.optica.org/oe/fulltext.cfm?uri=oe-17-20-17970}{\color{blue} O.E.} {\color{color-detail} \footnotesize \#tightly focus \#$\bar{\bar{\boldsymbol{\varepsilon}}}$ anisotropy} $|$ \href{http://www.nature.com/articles/s41377-020-00362-z}{\color{blue} Light.Sci.App.} $|$ \href{https://opg.optica.org/abstract.cfm?URI=oe-26-8-9840}{\color{blue} O.E.} } & 2023.02 \newline \vspace{7pt} \href{https://github.com/ChenZhu-Xie/PhD_academia/blob/master/1__Group_Meeting/6.1__\%E6\%B0\%B4\%E5\%BD\%A9\%E8\%8A\%B1\%E9\%B8\%9F_\%E2\%86\%90_Python__3.0_year_-_2023.3.27.pdf}{\raisebox{-0.05\height}{\color{black!50}\faGithub}} \\ \Gap\Gap\Gap
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%	\textbf{Real Scalar Nonlinear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} & \textbf{Closed-form} \colorbox{white}{\small $ {\color{magenta} E_3 \! \left( \boldsymbol r \right)} $} in \dbox{\colorbox{white}{\small $\left( \boldsymbol{\nabla}^2 + k^{2}_{3} \right) \! {\color{magenta} E_3 \! \left( \boldsymbol r \right)} = - k^{2}_{03} \;\! \chi(\boldsymbol r) E_1(\boldsymbol r) E_2(\boldsymbol r)$}} \newline \vspace{3pt} $\bullet$ {\small Solving multivariable/field nonlinear convolution equations directly on my own} \newline \vspace{-3pt} $\bullet$ {\small Strong alternative to Green's Function, pseudo-spectral, split-step Fourier methods} \newline \vspace{-3pt} $\bullet$ {\small Reproduced well-known papers \& models with higher both accuracy \& efficiency:} \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.143901}{\color{blue} P.R.L.} {\color{color-detail} \footnotesize \#Green} $|$ \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.023603}{\color{blue} P.R.L.} {\color{color-detail} \footnotesize \#experiment \#quantum} $|$ \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.93.133904}{\color{blue} P.R.L.} {\color{color-detail} \footnotesize \#experiment \#scatter} $|$ \href{https://link.aps.org/doi/10.1103/PhysRevLett.120.067601}{\color{blue} P.R.L.} } \newline \vspace{-3pt} \hspace{10pt} $\circ$ {\small \href{https://onlinelibrary.wiley.com/doi/10.1002/lpor.201900321}{\color{blue} L.P.R.} {\color{color-detail} \footnotesize \#SSF \#quantum} $|$ \href{https://sourceforge.net/projects/rcwa-1d/files/anisotropic_rcwa}{Matlab} {\color{color-detail} \footnotesize \#RCWA} $|$ \href{http://aip.scitation.org/doi/10.1063/1.4934488}{\color{blue} A.P.L.} {\color{color-detail} \footnotesize \#femtosecond pump} $|$ \href{https://opg.optica.org/abstract.cfm?URI=ol-42-21-4387}{\color{blue} O.L.} $|$ \href{https://link.aps.org/doi/10.1103/PhysRevA.101.023834}{\color{blue} P.R.A.} } & 2022.02 \newline \vspace{4pt} \href{https://github.com/ChenZhu-Xie/postgraduate_academia/blob/main/1__Group_Meeting/4.1__NLAST_v1.0_\%E2\%86\%90_Python\%2BBookxNote_Pro__2.0_year_-_2022.3.4.pdf}{\raisebox{-0.05\height}{\color{black!50}\faGithub}} \\ \Gap\Gap
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%	\textbf{Real Scalar Nonlinear} \newline \vspace{-3pt} {\small Fourier Crystal Optics} & \textbf{Closed-form} {\small $ E_3 \! \left( \boldsymbol r \right) $} in {\small $\left( \boldsymbol{\nabla}^2 + k^{2}_{3} \right) \! E_3 \! \left( \boldsymbol r \right) = - k^{2}_{03} \;\! \chi(\boldsymbol r) E_1(\boldsymbol r) E_2(\boldsymbol r)$} & 2017.03\hfill\textendash\hfill 2018.09 \newline \phantom{d} \newline \small Python $|$ SiYuan $|$ Mathematica \\ \Gap\Gap
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%	\large \multirowcell{1}[0ex][r]{\textbf{Memberships}} \phantom{d} & test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test test & 2017.03\textendash 2018.9 \\ \Gap
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